Interpolation, approximation and differentiation in the class of functions with compactly supported spectra (Q1975114)

In the paper the authors have used the sampling theorem to develop interpolation and approximation methods in the class of entire analytic functions, and the corresponding errors are estimated from above. Formulas for multiple differentiation of functions with compactly supported spectra, specified in terms of their samples on a nonuniform interpolation grid, are found; the corresponding differentiation errors are estimated from above. The applicability of the results is demonstrated for arbitrary functions that can be approximated by functions with compactly supported spectra to a given accuracy.